Relaxation filter options and how to use them

This page summarizes the practical control parameters for the TRANSP profile relaxation filter, the meaning of each option, and recommended settings for reduced-transport and predictive PT_SOLVER applications.

What the filter is doing

The filter modifies the profile that is passed into the anomalous transport model during a PT_SOLVER step. It blends radial smoothing, optional temporal anchoring, optional robust weighting, and optional shape control.

For profiles that are not evolved, the filtered result is used only inside the transport step and the original experimental profile is restored afterward. Repeated filtering therefore does not accumulate as a persistent time-history change in the stored profile.

The filter should be viewed as a transport-input regularization tool, not as a replacement for experimental data. Its purpose is to reduce numerical artifacts while preserving physically important profile structure and gradients.

Operational consequence

Use radial smoothing and soft shape filtering mainly to improve the transport solver numerics. Avoid using the filter to hide a physically inconsistent input setup. After changing relaxation parameters, compare the resulting transport-input profiles, effective diffusivities, and evolved temperatures against a baseline case.

Use lam_t_base carefully. For non-evolved profiles it influences the transport input used at the current step, but it does not create a lasting lagged profile state. For evolved profiles, temporal anchoring can help regularize the first predictive steps, but large values may delay the response of the profile to the transport model.

Main control parameters

Parameter	Role	Suggested starting range	Increase it to...	Main risk
`relx_profile`	Blend factor between the raw and filtered profile.	`0.2-1.0`	Apply more of the filtered result.	Over-filtering if the raw profile is already well behaved.
`lam_t_base`	Temporal smoothness or anchoring strength.	`0-1` for non-evolved profiles; `1-60` for stronger anchoring when needed.	Reduce step-to-step variation.	The transport input may follow previous frames too strongly and lag rapid physical changes.
`lam_r_base`	Radial curvature smoothing strength.	`0.1-10` for routine use; larger values should be treated as case-specific.	Reduce grid-scale roughness and stabilize gradients.	Broadening or damping real radial structure.
`shape_mode`	Shape constraint mode: `0` none, `1` hard monotone, `2` soft monotone.	`0`, `1`, or `2`.	Apply stronger shape control.	Hard mode can flatten profile features and alter gradients.
`lam_m_base`	Strength of the soft monotonicity penalty.	`1-20`	Suppress larger outward rises while avoiding hard projection.	Can erase real off-axis features if too large.
`delta_base`	Allowed outward increase before the soft monotone penalty activates.	`0.005-0.03` for soft density filtering; `0` for near-monotone behavior.	Preserve mild bumps or hollowness.	If too large, shape control becomes weak.
`bdy_weight`	Relative weight of edge adherence.	`0.5-2`, usually near `1`.	Hold the edge closer to the experimental value.	If too small, the edge can drift under curvature smoothing.

Recommended default strategy

For density and other non-evolved experimental profiles, prefer soft shape control with modest radial smoothing.
Use shape_mode = 2 for bump-preserving soft monotonicity.
Use delta_base > 0 to allow physically reasonable outward increases.
Keep bdy_weight near unity unless you intentionally want weak edge adherence.
Add temporal anchoring only after the radial and shape settings have been tuned.

No shape constraint

shape_mode = 0

Use only radial smoothing and optional temporal anchoring. This is a good choice for well-behaved profiles or for cases where non-monotone structure is expected to be physical.

Hard monotone

shape_mode = 1

Applies a monotone projection after the main solve. Use only when strict monotonicity is physically appropriate and flattening of local features is acceptable.

Soft monotone

shape_mode = 2

Adds a penalty for outward increases larger than delta_base. This is usually the preferred option for density filtering because it suppresses clearly problematic structure while preserving mild bumps and gradients more faithfully than hard monotone projection.

How to use the filter in practice

1. Start with the use case

Decide whether the profile is evolved by PT_SOLVER, fixed during prediction, or restored after each step. For restored experimental profiles, treat the filter as a within-step transport-input modifier.

2. Choose the shape policy

Use shape_mode = 2 for density unless you have a strong reason to enforce strict monotonicity. Use shape_mode = 0 when off-axis structure, pellet effects, internal transport barriers, or other non-monotone features are expected to be physical.

3. Tune smoothness first

Adjust lam_r_base until small-scale roughness is reduced without broadening the profile excessively. Check the resulting gradients, not only the profile values.

4. Add temporal anchoring last

Add only enough lam_t_base to reduce jitter in the transport input. Keep it low for non-evolved profiles unless frame-to-frame noise is clearly affecting convergence.

Suggested starting points

Case	Suggested setup
Experimental density, not evolved	`shape_mode = 2`, modest `lam_r_base`, small or zero `lam_t_base`, moderate `lam_m_base`, `delta_base = 0.01-0.03`.
Evolving predictive profile at the first predictive step	Use modest radial smoothing and, if needed, temporal anchoring to regularize the initial state. Avoid continuous aggressive filtering unless solver-generated artifacts persist.
Fixed profile used during prediction	Use soft shape control and modest radial smoothing. Use small temporal anchoring only if frame-to-frame jitter affects convergence.
Well-behaved profile with only minor noise	`shape_mode = 0`, small `lam_r_base`, little or no `lam_t_base`.
Need strict monotonicity	`shape_mode = 1` only if flattening is acceptable and physically consistent.

Transition-stage solver relaxation

Profile filtering can be combined with temporary relaxation of nonlinear convergence controls during the handoff from interpretive to predictive evolution. This transition is often the most difficult part of a predictive run, because the solver is reconciling a measurement-constrained state with transport-model-implied fluxes.

The recommended policy is staged strictness: use relaxed convergence only during the initial adjustment phase, then return to the standard solver settings once the profiles and diffusivities become smoother. Filtering and relaxation should be used together carefully. The filter removes profile-driven numerical pathologies, while temporary relaxation avoids excessive work on the remaining transient mismatch.

Residuals and Peclet-number-related factors

Recent PT_SOLVER refactoring changed the interpretation of enhancement factors and residuals used in diffusivity calculations. The default settings for residual and Peclet-number-related factors have also been updated. Most users do not set these quantities explicitly and should use the release defaults.

Users who explicitly set pt_residual%RES_TE, pt_residual%RES_TI, pt_residual%RES_NE, pt_residual%RES_NMAIN, pt_residual%RES_NIMP, pt_residual%RES_PPHI, or numerical-diffusivity parameters entering the Peclet-number calculation should review their input files before rerunning older cases. Values copied from older runs may not have the same practical meaning after the refactoring.

Use the current release defaults unless a convergence study indicates that changes are needed.
Do not increase residual tolerances only to make a run finish faster without checking profile fidelity.
Do not change Peclet-number factors or minimum numerical diffusivities unless the numerical behavior is understood.
When changing these values, compare electron temperature, ion temperature, density, rotation, effective diffusivities, and convective velocities against a baseline run.

For the broader PT_SOLVER setup, see the PT_SOLVER options page. For the algorithmic background, see arXiv:2605.09720.

When to be cautious

shape_mode = 1 can flatten local structure because it applies a hard monotone projection.
Large lam_m_base with very small delta_base can suppress real off-axis features.
Large lam_t_base can make the transport input follow previous frames too strongly.
Too small bdy_weight can let curvature regularization distort the edge.
Too much filtering can change gradient scale lengths and therefore change gradient-sensitive transport predictions.

Quick troubleshooting

Profile still noisy: raise lam_r_base first, then consider a small lam_t_base.
Real bump disappeared: reduce lam_m_base, increase delta_base, or set shape_mode = 0.
Edge shifted too much: increase bdy_weight.
Profile looks flattened: check whether shape_mode = 1 is active.
Transport input lags frame-to-frame: reduce lam_t_base.
Run is still slow after filtering: check nonlinear iterations, time-step cuts, and whether temporary transition-stage relaxation is active.

Bottom line

For reduced transport with experimental profiles that are restored after each step, the most robust operating point is usually:

shape_mode = 2 + modest lam_r_base + moderate lam_m_base + nonzero delta_base + bdy_weight near unity + little or no lam_t_base.

This keeps the transport input numerically smoother while preserving the essential profile shape more faithfully than hard monotone filtering. For evolved predictive profiles, use filtering mainly to regularize the initial state or to remove clear numerical artifacts, and avoid repeated aggressive filtering unless it is justified by convergence tests.